Calculus Calculator

“calculus is the most powerful weapon of thought, yet devised by the wit of man”.

It is no wonder that calculus is one of the most mind-boggling concepts in mathematics assignments and requires huge time, effort, and dedication from students. Unfortunately, even after that, some students fail to achieve to desired results due to lack of assistance. And it is right where our calculus calculator comes to the rescue.

Students have no option other than to solve mathematical problems. However, they can't devote numerous hours to one particular subject after attending regular classes and taking notes in the classroom. Hence, to ease the burden of the students, MyAssignmenthelp.com has launched its online calculus calculator.

Want to learn more about it? Continue scrolling down.

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What is the Fundamental Theorem of Calculus Calculator?

According to the Fundamental Theorem of Calculus calculator. Suppose f is continuous on [a,b].

If P(x)=∫xaf(t)dt, then P′(x)=f(x).

∫baf(x)dx=F(b)−F(a) where F is any antiderivative of f, that is F′=f.

Part 1 can be rewritten as ddx∫xaf(t)dt=f(x), which says that if f is integrated and the result is differentiated, we arrive back at the original function.

Part 2 can be rewritten as ∫baF′(x)dx=F(b)−F(a) and it says that if we take a function F, first differentiate it, and then integrate the result, we arrive back at the original function F, but in the form F(b)−F(a).

The Fundamental Theorem of Calculus says that differentiation and integration are inverse processes.

The fundamental theorem of calculus is a theorem that connects a function differentiation notion with the idea of integrating a function (calculating the gradient) (calculating the area under the curve). Thus, the two procedures are inverses, except a constant number depending on where you start calculating the area.

The First Portion

The first portion of the theorem, which is often termed the first basic calculus theorem, asserts that the integral f off, with a variable limit of integration, may be derived from one of the anti-derivates (also known as the indefinite integral) of certain functions, F. This means that anti-derivatives are available for continuous operations.

The Second Portion

In contrast, the second half of the theorem, also known as the second basic calculus theorem, asserts that the integral of a function f over certain intervals may be calculated using one of, say, F, its infinitely numerous anti-derivatives. The main practical application of this theorem is that the explicit determination of the function's anti-derivative via symbolic integration eliminates numerical integration in computational integrals.

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What is an Arc Length Calculus Calculator?

The emergence of infinitesimal calculus led to a generic formula that, in certain instances, offers closed-form answers.

Imagine finding the curve length between two spots (the derivative is continuous).

First, we divide the curve into tiny segments and apply the 2-points distance calculation for a rough answer for each length:

The distance from x₀ to x₁ is:

S₁ = √ (x₁ − x₀)² + (y₁ − y₀)²

Now, if we use Δ (delta) to calculate the mean of the difference between the given values using arc length calculus calculator, then we get-

S₁ = √ (Δx₁)² + (Δy₁)²

In this way we can get lot of more-

S₂ = √(Δx₂)² + (Δy₂)²

S₃ = √(Δx₃)² + (Δy₃)²

...

S_n = √(Δx_n)² + (Δy_n)²

One line using a Sum will add up the entire thing:

But still, there is a huge number of calculations!

The following plan may work

have all the Δx_ibe the same so that we can extract them from inside the square root
And then, we may turn the given sum into a particular integral.

Let's go:

First, divide and multiply Δy_i by Δx_i:

Now factor out (Δx_i)²:

Take (Δx_i)² out of the square root:

Now, as n approaches infinity:

We now have an integral also we may write dx to mean the Δx slices are approaching zero in width:

And dy/dx is the derivative of the function f(x), which can also be written f’(x):

The Arc Length Formula

So, the final steps can be summarized as-

Finding the derivative of f’(x)
Solving the integral of √1 + (f’(x))²dx

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How to use Volume Calculator Calculus?

A curve around the x-axis or yy-axis may produce several three-dimensional solids. For instance, if we turn the semi-circle provided by the xx-axis, we get a sphere of an RR radius. The classic formula for this sphere's volume may be derived.

Finding the Volume of a Sphere

We can consider a cross-section with a circle with radius f(x)f(x) and area π[f(x)]2π[f(x)]^2. We can consider each disc to have an infinitesimal thickness dx dx; the volume of each disc is approximately π[f(x)] ^2dxπ[f(x)] ^2dx. On adding up all these pieces in a volume calculator calculus, the sum will be-

This is often given the name of Method of Discs. In general, suppose y=f(x)y=f(x) is nonnegative and continuous on [a,b][a,b]. If the total and the entire given region is found to be bounded by the graph of ff, below by the x-axis, and on the sides by x=ax=a and x=bx=b is revolved about the x-axis, the volume VV of the generated solid is given by V=∫abπ[f(x)] 2dx.V=∫baπ[f(x)]2dx.

In this way, volume calculator calculus can be used for almost all solid shapes to calculate their volume. This helps to understand the volume of any small objects in a few simple steps.

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How to Use a Calculus Calculator with Steps

By utilizing your online calculus calculator, you can solve most limits and calculate issues.

This is what you do. Take a number very close to 5 and input it in x. If you have a TI84 calculator of Texas Instruments, perform these steps:

First, enter your home screen number, say 4.9999.
Next, press the Stop button, the x button, and the Enter button.
This will save the number in x.
Hit Enter.
The result, 9,9999, is quite near to several rounds, 10, that's your solution.
Store 4.999999 in x for proper measurement.
Follow the step 2 process.
Hit 2nd, Enter, 2nd, Enter, scroll back to function.
Hit Enter once again.
99999 — much closer to 10.
Try another number if you still have any concerns.
Store 4.99999999 in x, scroll down and hit Enter.
The outcome, 10, will clinch it.

(At 4.9999999, the function value is not 10, but it is so near that the calculator rounds up 10.)

By the way, if you use a different calculator model, you can probably accomplish the same or something similar to the same method.

Furthermore, like any other exam, ap calculus bc requires preparation and practice. Use our ap calculus bc score calculator to achieve the best results.

So, use the online Calculus calculator from MyAssignmenthelp.com, as it works as a: